Ratio and proportion method
H ere are several aids that will help you solve word problems:
1.
Make sure you understand the question that is asked
2.
Sort out the information to make a basic percent problem, such as “30% of what is 17?”
3.
Sometimes, you will have to subtract or add some of the numbers.
4.
The base will always be the original number, price, or total.
Some examples of percent word problems.
A baseball pitcher won 80% of the games he pitched. If he pitched 35 ballgames, how many games did he win?
80% of 35 is what?
80
100 35
1. Multiply the opposites
80 x 35 = 2800
2. Divide by the remaining number
28
100 2800
28 games
Jerry, an electrician, worked 7 months out of the year. What percent of the year did he work? (round answer to the nearest hundredth)
What percent of 12 is 7? 12 months = 1 year
100
7
12
1. Multiply the opposites
7 x 100 = 700
2. Divide by the remaining number
58.33
12 700.00
58.33% (rounded to hundredth)
Percent Word Problems Handout
Revised @2009 MLC page 1 of 8

Sometimes the information needed to solve a percent word problem is not stated directly. You will need to sort out the numbers given in the problem.
Organizing all the information into a box format will help you see what numbers you have and what you need.
Some examples.
There are 28 students in a class. Sixteen of those students are men.
What percent of the class are women? (Round to the nearest tenth)
Men % 16
Women % 12
Total 100% 28
12 is what % of 28?
100
12
28
1.
Multiple the opposites
100 x 12 = 1200
2.
Divide by the remaining number
42.85
28 1200.00
42.9%
`
Donovan took a math test and got 35 correct and 10 incorrect answers.
What was the percentage of correct answers? (Round to the nearest hundredth)
Correct answers % 35
Incorrect answers % 10
Total answers 100% 45
35 is what % of 45?
100
35
45
1.
Multiple the opposites
100 x 35 = 3500
2. Divide by the remaining number
77.777
45 3500.000
77.78% (rounded to hundredth)
Percent Word Problems Handout
Revised @2009 MLC page 2 of 8

Percent Word Problems
Directions: Set up a basic percent problem. Sometimes you will have to do extra steps to solve the problem. Follow rounding directions. Answers and solutions start on page 6.
1) A student earned a grade of 80% on a math test that had
20 problems. How many problems on this test did the student answer correctly? (round to the nearest whole number)
2) There are 36 carpenters in a crew. On a certain day, 29 were present. What percent showed up for work? (round to the nearest tenth)
3) A metal bar weighs 8.15 ounces. 93% of the bar is silver.
How many ounces of silver are in the bar? (round to the nearest thousandth)
4) A woman put $580 into a savings account for one year. The rate of interest on the account was 6½%. How much was the interest for the year in dollars and cents? (Round to the nearest cent)
Percent Word Problems Handout
Revised @2009 MLC page 3 of 8

5) A student answered 86 problems on a test correctly and received a grade 98%. How many problems were on the test, if all the problems were worth the same number of points?
(Round to the nearest whole number)
6) Manuel found a wrecked Trans-Am that he could fix. He bought the car for 65% of the original price of $7200.
What did he pay for the car? (Round to nearest dollar)
7) Pamela bought an electric drill at 85% of the regular price.
She paid $32.89 for the drill. What was the regular price?
(Round to the nearest cent)
8) A crew is made up of 8 men; the rest are women. 66 2 the crew are men. How many people are in the crew?
3
% of
9) Ben earns $12,800 a year. About 15% is taken out for taxes.
How much is taken out for taxes?
Percent Word Problems Handout
Revised @2009 MLC page 4 of 8

10) At a sale, shirts were sold for $15 each. This price was 80% of their original price. What was the original price?
11) There are 32 students in a class. Nine of those students are women. What percent are men? (round to the nearest tenth)
12) The Royals softball team played 75 games and won 55 of them. What percent of the games did they lose? (round to the nearest tenth)
Percent Word Problems Handout
Revised @2009 MLC page 5 of 8

1.
80
100 20
2.
100
29
36
3.
93
100 8.15
4.
6 1
2
100 580
5.
98
100
86
Answer Key
Multiply the opposites:
80 x 20 = 1600
Divide by the remaining number:
16
100 1600
16 problems
Multiply the opposites:
29 x 100 = 2900
Divide by the remaining number:
36
80 .
55
2900 .
00
80.6%
Multiply the opposites:
93 x 8.15 = 757.95
Divide by the remaining number:
100
7 .
5795
757 .
9500
7.580 ounces
Multiply the opposites:
6 ½ x 580 = 3770
Divide by the remaining number:
100
37 .
70
3770 .
00
$37.70
Multiply the opposites:
100 x 86 = 8600
Divide by the remaining number:
98
87 .
7
8600 .
0
88 problems (rounded to nearest whole)
Percent Word Problems Handout
Revised @2009 MLC page 6 of 8

6.
65
100 7200
7.
85
100
32.89
8.
66 2
100
3
8
9.
15
100 12,800
10.
80
100
15
Multiply the opposites:
65 x 7200 = 468,000
Divide by the remaining number:
100
4680
468000
$4680
Multiply the opposites:
100 x 32.89 = 3289
Divide by the remaining number:
85
38 .
694
3289 .
000
$38.69
Multiply the opposites:
100 x 8 = 800
Divide by the remaining number:
4
800 66
2
3
800
1
200
3
800
1
12
Multiply the opposites:
15 x 12,800 = 192,000
3
200
1
Divide by the remaining number:
100
1920
192000
$1920
Multiply the opposites:
100 x 15 = 1500
Divide by the remaining number:
80
18 .
75
1500 .
00
12
1
Percent Word Problems Handout
Revised @2009 MLC page 7 of 8

11.
Total
Men
Women
12.
Total
Won
Lost
100%
100
100
32
23
9
23
32
100% 75
55
20
20
75
$18.75
32
9
23
Multiply the opposites:
100 x 23 = 2300
Divide by the remaining number:
71.87
32 2300.00
71.9%(rounded to nearest tenth)
75
55
20
Multiply the opposites:
100 x 20 = 2000
Divide by the remaining number:
26.667
75 2000.000
26.7% games lost (rounded to tenth)
Percent Word Problems Handout
Revised @2009 MLC page 8 of 8